Finite Group Databasebeta

← #27089280

Subgroups — #27089280

Order 12032.

2168 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256684C211yesmaximal, characteristic, complemented
2C2×#15689673C211yesmaximal, characteristic, complemented
3#20254776C212yesmaximal, complemented
4#20254769C212yesmaximal, complemented
5#20254751C214yesmaximal, complemented
6#20254715C214yesmaximal, complemented
7#20254705C212yesmaximal, complemented
8#20254698C212yesmaximal, complemented
9#20253204C212yesmaximal, complemented
10#20253187C212yesmaximal, complemented
11#20253007C214yesmaximal, complemented
12#20252869C212yesmaximal, complemented
13#20252854C212yesmaximal, complemented
14C2×C47×#423C211yesmaximal, characteristic, complemented
15C22×#10625350—21no—
16C2×#13094052C2214yes—
17#15689680C2211yescharacteristic
18#15689680C2211yescharacteristic, complemented
19#15689680C2211yescharacteristic, complemented
20#15689673—21no—
21#15689673—21no—
22#15689673—21no—
23#15689673—21no—
24#15689673C2211yescharacteristic
25#15689673C2212yes—
26#15689673C2212yes—
27#15689673C2212yes—
28#15689673C2212yes—
29#15689673C2211yescharacteristic, complemented
30#15689673C2211yescharacteristic, complemented
31C2×#13094024C2211yescharacteristic
32C2×#13094021C2211yescharacteristic
33#15689657—21no—
34#15689657—21no—
35#15689657—21no—
36#15689657—21no—
37#15689657C2212yescomplemented
38#15689657C2212yescomplemented
39C2×#13094012—21no—
40#15689634—21no—
41#15689634—21no—
42#15689634C2212yes—
43C2×#13093998—21no—
44C2×#13093998C2212yes—
45C4×#10625350—21no—
46C4×#10625350—21no—
47C4×#10625350C2212yes—
48C2×C4×D188—21no—
49C2×C4×D188C2212yes—
50#15689424C2218yescomplemented
51#15689419C2214yescomplemented
52#15689414C2214yescomplemented
53#15689414C2214yescomplemented
54#15689409C2214yescomplemented
55#15689404C2214yescomplemented
56#15689404C2214yescomplemented
57#15689376C2218yescomplemented
58#15689369C2218yescomplemented
59#15689359C2218yescomplemented
60#15689352C2218yescomplemented
61#15689339C2218yescomplemented
62#15689329C2214yescomplemented
63#15689324C2214yescomplemented
64#15689324C2214yescomplemented
65#15689319C2214yescomplemented
66#15689319C2214yescomplemented
67#15689319C2214yescomplemented
68#15689165C2214yes—
69#15689129C2214yes—
70#15689125C2214yes—
71C22×M16×C47C2212yes—
72C22×C42×C47C2211yescharacteristic
73C47×#423C2212yes—
74C47×#423C2212yes—
75C47×#423C2212yescomplemented
76C47×#423C2212yescomplemented
77C2×C4⋊C8×C47C2212yescomplemented
78C2×C4⋊C8×C47C2212yescomplemented
79C2×#10625350—21no—
80C2×#10625350—21no—
81C2×#10625350—22no—
82C2×#10625350—22no—
83C2×#10625350—22no—
84C2×#10625350—22no—
85C2×#10625350—48no—
86C2×#10625350C2312yes—
87C22×Dic94—21no—
88C22×D188—21no—
89C22×D188—21no—
90C22×D188C2312yes—
91C22×C22⋊D47—22no—
92C22×C4×D47—22no—
93#13094052—48no—
94C2×#10625325C2318yes—
95C2×D376C2318yes—
96#13094024—21no—
97#13094024—21no—
98#13094024C2311yescharacteristic
99#13094024C2311yescharacteristic
100#13094024C2312yes—
101#13094024C2312yes—
102#13094024C2311yescharacteristic
103#13094021—21no—
104#13094021—21no—
105#13094021C2311yescharacteristic
106#13094021C2312yes—
107#13094021C2312yes—
108#13094018—22no—
109#13094018—22no—
110#13094016—21no—
111#13094016—21no—
112#13094016C2312yes—
113#13094012—22no—
114#13094012—22no—
115#13094012—22no—
116#13094012—22no—
117#13094012—21no—
118#13094012—21no—
119#13094012C2312yes—
120#13094007—22no—
121#13094007—22no—
122#13094007—22no—
123#13094003—21no—
124#13094003—21no—
125#13094003—21no—
126#13094003—21no—
127#13094003C2312yes—
128#13094003C2312yes—
129#13093998—22no—
130#13093998—22no—
131#13093998—22no—
132#13093998—22no—
133#13093998—22no—
134#13093998—22no—
135#13093998—21no—
136#13093998—21no—
137#13093998—21no—
138#13093998—21no—
139#13093998C2314yes—
140#13093998C2312yes—
141#13093998C2314yes—
142#13093998C2312yes—
143#13093993—22no—
144C4×Dic94—21no—
145C4×Dic94—21no—
146C4×Dic94—21no—
147C4×Dic94—21no—
148C4×Dic94C2312yes—
149C4×Dic94C2312yes—
150C4×D188—22no—
151C4×D188—22no—
152C4×D188—22no—
153C4×D188—22no—
154C4×D188—22no—
155C4×D188—22no—
156C4×D188—21no—
157C4×D188—21no—
158C4×D188—21no—
159C4×D188—21no—
160C4×D188C2312yes—
161C4×D188C2312yes—
162C4×D188C2314yes—
163C4×D188C2314yes—
164C4×C22⋊D47—22no—
165C4×C22⋊D47—22no—
166C4×C22⋊D47—22no—
167C4×C22⋊D47—22no—
168C4×C22⋊D47—22no—
169C4×C22⋊D47—22no—
170#13093983—21no—
171#13093983—21no—
172#13093983C2312yes—
173#13093981—22no—
174#13093981—22no—
175#13093981—22no—
176C2×C4⋊Dic47—21no—
177C2×C4⋊Dic47C2312yes—
178C2×(C2×D47)⋊C4—22no—
179C2×(C2×D47)⋊C4—22no—
180C42×D47—22no—
181#13093958C2318yes—
182#13093956C2318yes—
183#13093949C2318yes—
184#13093946C2318yes—
185#13093946C2318yes—
186#13093946C2318yes—
187C23×C4×C47D411yescharacteristic
188C23×C4×C47D411yescharacteristic
189C23×C4×C47C2311yescharacteristic
190C2×M16×C47—44no—
191C2×M16×C47C2314yes—
192C2×M16×C47C2314yes—
193C22×C8×C47C2314yes—
194C2×C42×C47D411yescharacteristic
195C2×C42×C47D411yescharacteristic
196C2×C42×C47D411yescharacteristic
197C2×C42×C47D411yescharacteristic
198C2×C42×C47D411yescharacteristic
199C2×C42×C47D411yescharacteristic
200C2×C42×C47C2311yescharacteristic
201C2×C42×C47C2311yescharacteristic
202C2×C42×C47C2311yescharacteristic
203C2×C42×C47C2311yescharacteristic
204C2×C42×C47C2311yescharacteristic
205C2×C42×C47C2311yescharacteristic
206C4⋊C8×C47C2314yes—
207C4⋊C8×C47C2314yes—
208C4⋊C8×C47C2314yes—
209C4⋊C8×C47C2314yes—
210C24×C47C2×D411yescharacteristic
211C23×D47—22no—
212C22×C4×C47—24no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—42no—
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2411yescharacteristic
232C22×C4×C47C2411yescharacteristic
233C22×C4×C47C2411yescharacteristic
234C2×C22⋊D47—22no—
235C2×C22⋊D47—22no—
236C2×C22⋊D47—22no—
237C2×C22⋊D47—24no—
238C2×C22⋊D47—24no—
239C2×C22⋊D47—48no—
240C22×Dic47—22no—
241#10625350—24no—
242#10625350—24no—
243#10625350—44no—
244#10625350—48no—
245#10625350—48no—
246#10625350—48no—
247#10625350—44no—
248#10625350—48no—
249C2×D188—24no—
250C2×D188—24no—
251C2×D188—21no—
252C2×D188—21no—
253C2×D188—22no—
254C2×D188—22no—
255C2×D188—22no—
256C2×D188—22no—
257C2×D188—22no—
258C2×D188—44no—
259C2×D188—44no—
260C2×D188C2412yes—
261C2×D188C2414yes—
262C2×C4×D47—22no—
263C2×C4×D47—22no—
264C2×C4×D47—22no—
265C2×C4×D47—24no—
266C2×C4×D47—24no—
267C2×C4×D47—48no—
268C2×Dic94—21no—
269C2×Dic94—21no—
270C2×Dic94—22no—
271C2×Dic94—22no—
272C2×Dic94—44no—
273C2×Dic94C2412yes—
274M16×C47—28no—
275M16×C47—44no—
276C2×C8×C47—44no—
277C2×C8×C47C2418yes—
278C42×C47C2×D411yescharacteristic
279C42×C47C2×D411yescharacteristic
280C42×C47C2×D411yescharacteristic
281C42×C47C2×D411yescharacteristic
282C42×C47C2×D411yescharacteristic
283C42×C47C2×D411yescharacteristic
284C42×C47C2×D411yescharacteristic
285C42×C47C2×D411yescharacteristic
286C42×C47C2×D411yescharacteristic
287C42×C47C2×D411yescharacteristic
288C42×C47C2×D411yescharacteristic
289C42×C47C2×D411yescharacteristic
290C42×C47C2411yescharacteristic
291C42×C47C2411yescharacteristic
292C42×C47C2411yescharacteristic
293C42×C47C2411yescharacteristic
294C22⋊Dic47—22no—
295C22⋊Dic47—22no—
296C22⋊Dic47—22no—
297(C2×D47)⋊C4—24no—
298(C2×D47)⋊C4—24no—
299(C2×D47)⋊C4—24no—
300(C2×D47)⋊C4—24no—
301(C2×D47)⋊C4—22no—
302(C2×D47)⋊C4—22no—
303(C2×D47)⋊C4—22no—
304(C2×D47)⋊C4—22no—
305(C2×D47)⋊C4—22no—
306(C2×D47)⋊C4—22no—
307C4⋊Dic47—22no—
308C4⋊Dic47—22no—
309C4⋊Dic47—22no—
310C4⋊Dic47—21no—
311C4⋊Dic47—21no—
312C4⋊Dic47—21no—
313C4⋊Dic47—21no—
314C4⋊Dic47C2412yes—
315C4⋊Dic47C2412yes—
316C4⋊Dic47C2414yes—
317Dic47⋊C4—22no—
318Dic47⋊C4—22no—
319Dic47⋊C4—22no—
320Dic47⋊C4—22no—
321Dic47⋊C4—22no—
322Dic47⋊C4—22no—
323C4×Dic47—22no—
324C4×Dic47—22no—
325C4×Dic47—22no—
326D376—48no—
327#10625325—48no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47—41no—
331C23×C47C22×D411yescharacteristic
332C23×C47C22×D411yescharacteristic
333C23×C47C22×D411yescharacteristic
334C22×D47—22no—
335C22×D47—24no—
336C22×D47—44no—
337C22×D47—44no—
338C22×D47—44no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—21no—
351C2×C4×C47—21no—
352C2×C4×C47—21no—
353C2×C4×C47—21no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47AGL(1,ℤ/8)14yescomplemented
358C2×C4×C47C22×D411yescharacteristic
359C2×C4×C47C22×D411yescharacteristic
360C2×C4×C47C22×D411yescharacteristic
361C2×C4×C47C22×D411yescharacteristic
362C2×C4×C47C22×D411yescharacteristic
363C2×C4×C47C22×D411yescharacteristic
364C2×C4×C47C22×D411yescharacteristic
365C2×C4×C47C22×D411yescharacteristic
366C2×C4×C47C22×D411yescharacteristic
367C2×C4×C47C22×D411yescharacteristic
368C2×C4×C47C22×D411yescharacteristic
369C2×C4×C47H(5,𝔽2)12yes—
370C2×C4×C472−1+412yes—
371C2×C4×C47C2511yescharacteristic
372C22⋊D47—48no—
373C22⋊D47—44no—
374C22⋊D47—44no—
375C22⋊D47—48no—
376C22⋊D47—44no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—24no—
381C2×Dic47—44no—
382D188—24no—
383D188—22no—
384D188—24no—
385D188—22no—
386D188—44no—
387D188—44no—
388D188—42no—
389D188—44no—
390D188—44no—
391D188—42no—
392D188—44no—
393C4×D47—48no—
394C4×D47—44no—
395C4×D47—48no—
396C4×D47—44no—
397C4×D47—44no—
398Dic94—22no—
399Dic94—22no—
400Dic94—44no—
401Dic94—42no—
402Dic94—44no—
403Dic94—42no—
404C8×C47—28no—
405#60916—471nomaximal, Sylow
406C22×C47—21no—
407C22×C47—21no—
408C22×C47—21no—
409C22×C47—21no—
410C22×C47—21no—
411C22×C47—21no—
412C22×C47—21no—
413C22×C47—44no—
414C22×C47#53712yes—
415C22×C47C2×AGL(1,ℤ/8)12yes—
416C22×C47C23×D411yescharacteristic
417C2×D47—42no—
418C2×D47—44no—
419C2×D47—44no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—44no—
423C2×D47—88no—
424C4×C47—21no—
425C4×C47—21no—
426C4×C47—21no—
427C4×C47—21no—
428C4×C47—21no—
429C4×C47—21no—
430C4×C47—21no—
431C4×C47#53712yes—
432C4×C47C2×AGL(1,ℤ/8)12yes—
433C4×C47C2×AGL(1,ℤ/8)12yes—
434C4×C47#57512yes—
435C4×C47C2×H(5,𝔽2)11yescharacteristic
436C4×C47C2×2−1+411yescharacteristic
437Dic47—42no—
438Dic47—44no—
439Dic47—42no—
440Dic47—42no—
441#3444—471no—
442C2×#532—471no—
443#3254—472no—
444#3253—472no—
445#3251—474no—
446#3247—474no—
447#3246—472no—
448#3245—472no—
449#3079—472no—
450#3077—472no—
451#3055—474no—
452#3038—472no—
453#3036—472no—
454C2×#423D4711yescharacteristic, complemented
455C2×C47—22no—
456C2×C47—22no—
457C2×C47—41no—
458C2×C47C2×#53711yescharacteristic
459C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
460C2×C47C2×#57511yescharacteristic
461D47—82no—
462D47—84no—
463C22×#41—941no—
464C2×AGL(1,ℤ/8)—474no—
465C22×M16C2×D4712yes—
466#533—471no—
467#533—471no—
468#533—471no—
469#532—472no—
470#532—472no—
471#532—472no—
472#532—472no—
473#532—471no—
474#532—471no—
475#532—471no—
476#532—941no—
477#532—941no—
478#532—941no—
479#532—941no—
480C2×C4⋊Q8—471no—
481C2×#127—471no—
482#529—472no—
483#529—472no—
484#529—941no—
485#529—941no—
486#529—941no—
487#529—941no—
488C2×#124—941no—
489#525—472no—
490#525—941no—
491#525—941no—
492C2×#121—472no—
493C2×#121—941no—
494C4×#41—472no—
495C4×#41—941no—
496C4×#41—941no—
497C2×C4×D4—472no—
498C2×C4×D4—941no—
499C22×C42C2×D4711yescharacteristic
500#478—478no—
501#477—474no—
502#476—474no—
503#476—474no—
504#475—474no—
505#474—474no—
506#474—474no—
507#469—478no—
508#468—478no—
509#466—478no—
510#465—478no—
511#463—478no—
512#461—474no—
513#460—474no—
514#460—474no—
515#459—474no—
516#459—474no—
517#459—474no—
518#428—474no—
519#423C2×D4712yes—
520#423C2×D4712yes—
521#423C2×D4712yescomplemented
522#423C2×D4712yescomplemented
523C2×C4⋊C8C2×D4712yescomplemented
524C2×C4⋊C8C2×D4712yescomplemented
525#418—474no—
526#417—474no—
527C47#6091611yescharacteristic, complemented, Sylow
528C2×#41—472no—
529C2×#41—941no—
530C2×#41—941no—
531C2×#41—942no—
532C2×#41—942no—
533C2×#41—942no—
534C2×#41—942no—
535C2×#41—1888no—
536C22×Q8—941no—
537C22×D4—472no—
538C22×D4—942no—
539C22×D4—941no—
540C22×D4—941no—
541C23×C4—942no—
542C23×C4D18811yescharacteristic
543C23×C4D18811yescharacteristic
544C23×C4C22×D4711yescharacteristic
545AGL(1,ℤ/8)—1888no—
546C2×SD16—478no—
547C2×D8—478no—
548C2×M16—44no—
549C2×M16C22×D4714yes—
550C2×M16C22×D4714yes—
551C22×C8C22×D4714yes—
552C4⋊Q8—472no—
553C4⋊Q8—472no—
554C4⋊Q8—471no—
555C4⋊Q8—471no—
556C4⋊Q8—471no—
557C4⋊Q8—941no—
558C4⋊Q8—941no—
559#127—472no—
560#127—472no—
561#127—471no—
562#127—941no—
563#127—941no—
564#126—942no—
565#126—942no—
566#125—472no—
567#125—941no—
568#125—941no—
569#124—472no—
570#124—942no—
571#124—942no—
572#124—942no—
573#124—942no—
574#124—941no—
575#124—941no—
576#123—942no—
577#123—942no—
578#123—942no—
579C22⋊Q8—472no—
580C22⋊Q8—472no—
581C22⋊Q8—941no—
582C22⋊Q8—941no—
583C22⋊Q8—941no—
584C22⋊Q8—941no—
585#121—474no—
586#121—474no—
587#121—472no—
588#121—472no—
589#121—942no—
590#121—942no—
591#121—942no—
592#121—942no—
593#121—942no—
594#121—942no—
595#121—941no—
596#121—941no—
597#121—941no—
598#121—941no—
599#120—942no—
600C4×Q8—472no—
601C4×Q8—472no—
602C4×Q8—941no—
603C4×Q8—941no—
604C4×Q8—941no—
605C4×Q8—941no—
606C4×D4—474no—
607C4×D4—474no—
608C4×D4—472no—
609C4×D4—472no—
610C4×D4—942no—
611C4×D4—942no—
612C4×D4—942no—
613C4×D4—942no—
614C4×D4—942no—
615C4×D4—942no—
616C4×D4—942no—
617C4×D4—942no—
618C4×D4—942no—
619C4×D4—942no—
620C4×D4—942no—
621C4×D4—942no—
622C4×D4—941no—
623C4×D4—941no—
624C4×D4—941no—
625C4×D4—941no—
626#117—472no—
627#117—941no—
628#117—941no—
629#117—942no—
630#117—942no—
631#117—942no—
632C2×C4⋊C4—472no—
633C2×C4⋊C4—941no—
634C2×C22⋊C4—942no—
635C2×C22⋊C4—942no—
636C2×C42—942no—
637C2×C42D18811yescharacteristic
638C2×C42D18811yescharacteristic
639C2×C42D18811yescharacteristic
640C2×C42D18811yescharacteristic
641C2×C42D18811yescharacteristic
642C2×C42D18811yescharacteristic
643C2×C42C22×D4711yescharacteristic
644C2×C42C22×D4711yescharacteristic
645C2×C42C22×D4711yescharacteristic
646C2×C42C22×D4711yescharacteristic
647C2×C42C22×D4711yescharacteristic
648C2×C42C22×D4711yescharacteristic
649#107—478no—
650#106—478no—
651C4⋊C8C22×D4714yes—
652C4⋊C8C22×D4714yes—
653C4⋊C8C22×D4714yes—
654C4⋊C8C22×D4714yes—
655#103—478no—
656#102—478no—
657#102—478no—
658#102—478no—
659C24—942no—
660C24C2×D18811yescharacteristic
661#41—944no—
662#41—944no—
663#41—1884no—
664#41—1888no—
665#41—1888no—
666#41—1888no—
667#41—1884no—
668#41—1888no—
669C2×Q8—472no—
670C2×Q8—941no—
671C2×Q8—941no—
672C2×Q8—942no—
673C2×Q8—942no—
674C2×Q8—1884no—
675C2×D4—472no—
676C2×D4—474no—
677C2×D4—942no—
678C2×D4—942no—
679C2×D4—942no—
680C2×D4—944no—
681C2×D4—944no—
682C2×D4—941no—
683C2×D4—941no—
684C2×D4—942no—
685C2×D4—942no—
686C2×D4—942no—
687C2×D4—942no—
688C2×D4—942no—
689C2×D4—944no—
690C2×D4—944no—
691C2×D4—1884no—
692C2×D4—1884no—
693C2×D4—1888no—
694C22×C4—24no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—42no—
698C22×C4—942no—
699C22×C4—942no—
700C22×C4—942no—
701C22×C4—942no—
702C22×C4—944no—
703C22×C4—944no—
704C22×C4—1888no—
705C22×C4C2×D18811yescharacteristic
706C22×C4C2×D18811yescharacteristic
707C22×C4C2×D18811yescharacteristic
708C22×C4C2×D18811yescharacteristic
709C22×C4C2×D18811yescharacteristic
710C22×C4C2×D18811yescharacteristic
711C22×C4C2×D18811yescharacteristic
712C22×C4C2×D18811yescharacteristic
713C22×C4C2×D18811yescharacteristic
714C22×C4C2×D18811yescharacteristic
715C22×C4C2×D18811yescharacteristic
716C22×C4C2×D18811yescharacteristic
717C22×C4C2×D18811yescharacteristic
718C22×C4C2×D18811yescharacteristic
719C22×C4C2×D18811yescharacteristic
720C22×C4C23×D4711yescharacteristic
721C22×C4C23×D4711yescharacteristic
722C22×C4C23×D4711yescharacteristic
723SD16—1888no—
724D8—1888no—
725M16—28no—
726M16—44no—
727C2×C8—44no—
728C2×C8C23×D4718yes—
729C4⋊C4—472no—
730C4⋊C4—472no—
731C4⋊C4—474no—
732C4⋊C4—942no—
733C4⋊C4—942no—
734C4⋊C4—942no—
735C4⋊C4—942no—
736C4⋊C4—942no—
737C4⋊C4—942no—
738C4⋊C4—942no—
739C4⋊C4—942no—
740C4⋊C4—942no—
741C4⋊C4—941no—
742C4⋊C4—941no—
743C4⋊C4—941no—
744C4⋊C4—941no—
745C22⋊C4—942no—
746C22⋊C4—942no—
747C22⋊C4—942no—
748C22⋊C4—944no—
749C22⋊C4—944no—
750C22⋊C4—944no—
751C22⋊C4—944no—
752C22⋊C4—942no—
753C22⋊C4—942no—
754C22⋊C4—942no—
755C22⋊C4—942no—
756C22⋊C4—942no—
757C22⋊C4—942no—
758C42—942no—
759C42—942no—
760C42—942no—
761C42C2×D18811yescharacteristic
762C42C2×D18811yescharacteristic
763C42C2×D18811yescharacteristic
764C42C2×D18811yescharacteristic
765C42C2×D18811yescharacteristic
766C42C2×D18811yescharacteristic
767C42C2×D18811yescharacteristic
768C42C2×D18811yescharacteristic
769C42C2×D18811yescharacteristic
770C42C2×D18811yescharacteristic
771C42C2×D18811yescharacteristic
772C42C2×D18811yescharacteristic
773C42C23×D4711yescharacteristic
774C42C23×D4711yescharacteristic
775C42C23×D4711yescharacteristic
776C42C23×D4711yescharacteristic
777C23—22no—
778C23—22no—
779C23—41no—
780C23—942no—
781C23—944no—
782C23—1884no—
783C23—1884no—
784C23—1884no—
785C23C22×D18811yescharacteristic
786C23C22×D18811yescharacteristic
787C23C22×D18811yescharacteristic
788Q8—942no—
789Q8—942no—
790Q8—1884no—
791Q8—1882no—
792Q8—1884no—
793Q8—1882no—
794D4—942no—
795D4—944no—
796D4—944no—
797D4—942no—
798D4—1884no—
799D4—1884no—
800D4—1882no—
801D4—1888no—
802D4—1884no—
803D4—1888no—
804D4—1884no—
805D4—1884no—
806D4—1884no—
807D4—1882no—
808D4—1884no—
809D4—1884no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—942no—
829C2×C4—942no—
830C2×C4—942no—
831C2×C4—944no—
832C2×C4—1888no—
833C2×C4—1884no—
834C2×C4—1888no—
835C2×C4—1884no—
836C2×C4—1884no—
837C2×C4—1884no—
838C2×C4#1309405214yescomplemented
839C2×C4C22×D18811yescharacteristic
840C2×C4C22×D18811yescharacteristic
841C2×C4C22×D18811yescharacteristic
842C2×C4C22×D18811yescharacteristic
843C2×C4C22×D18811yescharacteristic
844C2×C4C22×D18811yescharacteristic
845C2×C4C22×D18811yescharacteristic
846C2×C4C22×D18811yescharacteristic
847C2×C4C22×D18811yescharacteristic
848C2×C4C22×D18811yescharacteristic
849C2×C4C22×D18811yescharacteristic
850C2×C4#1309406912yes—
851C2×C4#1309407212yes—
852C2×C4C24×D4711yescharacteristic
853C8—28no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—44no—
862C22—3768no—
863C22—1884no—
864C22—1882no—
865C22—1882no—
866C22—1884no—
867C22—1882no—
868C22—1884no—
869C22#1568970412yes—
870C22C2×#1309405212yes—
871C22C23×D18811yescharacteristic
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—1884no—
880C4—1882no—
881C4—1882no—
882C4—1882no—
883C4#1568970412yes—
884C4C2×#1309405212yes—
885C4C2×#1309405212yes—
886C4#1568992312yes—
887C4C2×#1309406911yescharacteristic
888C4C2×#1309407211yescharacteristic
889C2—22no—
890C2—22no—
891C2—41no—
892C2—3764no—
893C2—3762no—
894C2C2×#1568970411yescharacteristic
895C2C22×#1309405211yescharacteristic
896C2C2×#1568992311yescharacteristic
subgroupG/H
centerC22C23×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#423C2
socleC22×C47C23×D4
hypercenterC2×#423D47
hypocenterC47#60916
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#423

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20256684C2semidirect
2. C2×#15689673C2semidirect
3. #20254776C2semidirect
4. #20254769C2semidirect
5. #20254751C2semidirect
6. #20254715C2semidirect
7. #20254705C2semidirect
8. #20254698C2semidirect
9. #20253204C2semidirect
10. #20253187C2semidirect
11. #20253007C2semidirect
12. #20252869C2semidirect
13. #20252854C2semidirect
14. C2×C47×#423C2semidirect
18. #15689680C22semidirect
19. #15689680C22semidirect
29. #15689673C22semidirect
30. #15689673C22semidirect
37. #15689657C22semidirect
38. #15689657C22semidirect
50. #15689424C22semidirect
51. #15689419C22semidirect
52. #15689414C22semidirect
53. #15689414C22semidirect
54. #15689409C22semidirect
55. #15689404C22semidirect
56. #15689404C22semidirect
57. #15689376C22semidirect
58. #15689369C22semidirect
59. #15689359C22semidirect
60. #15689352C22semidirect
61. #15689339C22semidirect
62. #15689329C22semidirect
63. #15689324C22semidirect
64. #15689324C22semidirect
65. #15689319C22semidirect
66. #15689319C22semidirect
67. #15689319C22semidirect
75. C47×#423C22semidirect
76. C47×#423C22semidirect
77. C2×C4⋊C8×C47C22semidirect
78. C2×C4⋊C8×C47C22semidirect
357. C2×C4×C47AGL(1,ℤ/8)semidirect
454. C2×#423D47semidirect
521. #423C2×D47semidirect
522. #423C2×D47semidirect
523. C2×C4⋊C8C2×D47semidirect
524. C2×C4⋊C8C2×D47semidirect
527. C47#60916semidirect
838. C2×C4#13094052semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202566842
C2×#156896732
#202547762
#202547692
#202547512
#202547152
#202547052
#202546982
#202532042
#202531872
#202530072
#202528692
#202528542
C2×C47×#4232
#6091647